In switched reluctance motor drives, the combination of power-electronic converter and a motor phase defines a resonant circuit, comprised by the motor phase inductance and the parasitic capacitance of converter switches, power cables and motor phase winding. If a motor phase is excited by applying very short voltage pulses, the resonance frequency of the circuit can be observed through the subsequent damped oscillation of the induced voltage in the phase. As the phase inductance and associated resonance frequency depend on the rotor position, the method provides a means for estimating the rotor position.
This paper discusses the influence of the magnetic inductive coupling between motor phases on the observed damped voltage resonance. It is shown that the motor-converter combination can be modelled as a system comprising different resonant circuits, each associated with one phase of the machine, which are mutually coupled due to the inductive coupling between the motor phases. An eigenvalue analysis reveals the different eigenfrequencies and modes of oscillation for this system. It follows from the analysis that damped voltage resonances occur in all phases of the machine due to the mutual coupling. The model is used to determine the influence of voltage pulses, applied to a single phase or simultaneously applied to different phases, on the observed damped voltage oscillations, and thus on the rotor position estimation.

@inproceedings{971289,
abstract = {In switched reluctance motor drives, the combination of power-electronic converter and a motor phase defines a resonant circuit, comprised by the motor phase inductance and the parasitic capacitance of converter switches, power cables and motor phase winding. If a motor phase is excited by applying very short voltage pulses, the resonance frequency of the circuit can be observed through the subsequent damped oscillation of the induced voltage in the phase. As the phase inductance and associated resonance frequency depend on the rotor position, the method provides a means for estimating the rotor position.
This paper discusses the influence of the magnetic inductive coupling between motor phases on the observed damped voltage resonance. It is shown that the motor-converter combination can be modelled as a system comprising different resonant circuits, each associated with one phase of the machine, which are mutually coupled due to the inductive coupling between the motor phases. An eigenvalue analysis reveals the different eigenfrequencies and modes of oscillation for this system. It follows from the analysis that damped voltage resonances occur in all phases of the machine due to the mutual coupling. The model is used to determine the influence of voltage pulses, applied to a single phase or simultaneously applied to different phases, on the observed damped voltage oscillations, and thus on the rotor position estimation.},
author = {Geldhof, Kristof and Van den Bossche, Alex and Melkebeek, Jan},
booktitle = {IECON : 2009 35th Annual conference of IEEE Industrial Electronics, vols 1-6},
isbn = {9781424446490},
issn = {1553-572X},
keywords = {Eigenfrequency,Mutual Coupling,Position Estimation,Switched Reluctance Motor,Eigenmode,Resonance},
language = {eng},
location = {Porto, Portugal},
pages = {4058--4064},
publisher = {IEEE},
title = {Influence of electrical eigenfrequencies on damped voltage resonance based sensorless control of switched reluctance drives},
url = {http://dx.doi.org/10.1109/IECON.2009.5415108},
year = {2009},
}